{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Malkmus Band Transmission Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>© Von P. Walden, Washington State University</i>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### This notebook approximates the transmission of the atmosphere using the equations for the Malkmus Random Band Model from Petty (2006), A First Course in Radiative Transfer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# y is the \"grayness parameter\" and is equal to aL / delta, where aL is the Lorentz line width \n",
    "#       and delta is the average line spacing.\n",
    "y   = 0.0001   # See Figure 10.3 in Petty (2006).\n",
    "Sud = arange(0.1,1000,0.001)\n",
    "\n",
    "# Calculate the transmission using the Malkmus model.\n",
    "T   = exp( (-pi*y/2.) * ( (1. + (4./(pi*y)) * Sud)**0.5 - 1. ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Transmission from Malkmus Random Model')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a plot of (S/d)u versus Band Transmittance \n",
    "figure(figsize=(12,6))\n",
    "semilogx(Sud,T)\n",
    "xlabel('Su/d')\n",
    "ylabel('Band Transmission')\n",
    "title('Transmission from Malkmus Random Model')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1267a4050>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#legend(('10','1.0','0.1','0.01','0.001','0.0001'),loc='best')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
